[Help] Why in one case you consider the initial purchase price and in the second case you don't?

Hereare the two questions side by side. In both cases the investor has a sunken cost, why is that only being factored into Question 53 and not Question 40?

In the first case the decision about the $400,000 investment is yet to be made. So the option value is basically the answer to the question “What is this project worth if I have to start from scratch (including buying the land)”.

In the second case he has already bought the land. Here the option value answers the question “What is a reasonable value of the land now?” (one use could be to find a reasonable selling price, if you do not want to do the project yourself).

If you alter the second case and say “He considers purchasing land for $650,000 to do a project, described as follows […]. What is the option value of the project?”, then the calculation you’d have to do would be equivalent to the first case.